If /BC bisects �ÚABD, and �ÚABC = 5x + 11, �ÚCBD = 10x − 4, then find x.
5
3
1
2
I am having trouble with this one, please help.
Your symbols did not come out as you expected, but I concluded that you said:
line BC bisects angle ABD, and angle ABC = 5x+11, angle CBD = 10x-4
so the two angles are equal, or
10x-4 = 5x+11
5x = 15
x = 3
check: angle ABC = 5(3) + 11 = 26
angle CBD = 10(3) - 4 = 26
YUP!!!
Thanks much, I did figure it out and appreciate your explanation.
To find the value of x in this problem, we can start by using the fact that /BC bisects �ÚABD.
By definition, when a line bisects an angle, it creates two congruent angles. In this case, we have the angles �ÚABC and �ÚCBD. So, we can set them equal to each other:
�ÚABC = �ÚCBD
Substituting the given values, we have:
5x + 11 = 10x - 4
Now, we can solve this equation for x.
First, we can move the terms with x to one side of the equation:
5x - 10x = -4 - 11
Combining like terms:
-5x = -15
Next, divide both sides of the equation by -5 to isolate x:
-5x / -5 = -15 / -5
Simplifying:
x = 3
Therefore, the value of x in this problem is 3.